A k-Almost Prime Number is a number having exactly k prime factors (not necessary distinct).
2, 3, 5, 7, 11 ….(in fact all prime numbers) are 1-Almost Prime Numbers as they have only 1 prime factors (which is themselves).
4, 6, 9…. are 2-Almost Prime Numbers as they have exactly 2 prime factors (4 = 2*2, 6 = 2*3, 9 = 3*3)
Similarly 32 is a 5-Almost Prime Number (32 = 2*2*2*2*2) and so is 72 (2*2*2*3*3)
All the 1-Almost Primes are called as Prime Numbers and all the 2-Almost Prime are called as semi-primes.
The task is to print first n numbers that are k prime.
Input : k = 2, n = 5 Output : 4 6 9 10 14 4 has two prime factors, 2 x 2 6 has two prime factors, 2 x 3 Similarly, 9(3 x 3), 10(2 x 5) and 14(2 x 7) Input : k = 10, n = 2 Output : 1024 1536 1024 and 1536 are first two numbers with 10 prime factors.
We iterate natural numbers and keep printing k-primes till the count of printed k-primes is less than or equal to n. To check if a number is k-prime, we find count of prime factors and if the count is k we consider the number as k-prime.
Below is the implementation of above idea :
First 10 2-almost prime numbers : 4 6 9 10 14 15 21 22 25 26
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